Theorems · Theorem · logic and foundations
hasCardinalLT_sum_iff
∀ (X : Type u) (Y : Type u') (κ : Cardinal.{w}),
Cardinal.aleph0 ≤ κ → (HasCardinalLT (X ⊕ Y) κ ↔ HasCardinalLT X κ ∧ HasCardinalLT Y κ)- Defined in
- Mathlib.SetTheory.Cardinal.HasCardinalLT
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- HasCardinalLTstatement and proof · cited by 99
- Cardinal.lift_liftproof · cited by 53
- Sum.inr_injectiveproof · cited by 40
- Cardinal.lift_ltproof · cited by 39
- Sum.inl_injectiveproof · cited by 39
- Cardinal.mk_sumproof · cited by 19
- Cardinal.lift_addproof · cited by 18
- HasCardinalLT.of_injectiveproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- hasCardinalLT_subtype_maxproof · cited by 1
- hasCardinalLT_option_iffproof · cited by 1